CN102930176A - Nine-grid five-spline interpolation method for geoid model - Google Patents
Nine-grid five-spline interpolation method for geoid model Download PDFInfo
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- CN102930176A CN102930176A CN2012104781311A CN201210478131A CN102930176A CN 102930176 A CN102930176 A CN 102930176A CN 2012104781311 A CN2012104781311 A CN 2012104781311A CN 201210478131 A CN201210478131 A CN 201210478131A CN 102930176 A CN102930176 A CN 102930176A
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Abstract
A method utilizing geoid grid interpolation for calculating height anomaly of any point belongs to the field of geodesy and measurement engineering technology. GPS (Global Positioning System) height measurement is currently the quickest high-precision height measurement method, however, the 1985 Yellow Sea normal height system in which the GPS ground height has to be converted into the normal height is adopted by China. The method provided by the invention, which is based on the geoid grid, utilizes the nine-grid five-spline interpolation to calculate the height anomaly. According to the method, based on nine grids and sixteen joints closest to a point for interpolation, four joints on the same straight line are respectively adopted to form four polishing spline curves which are used for calculating the height anomaly of the middle point, and then spline curves formed by the middle points are adopted to calculate the height anomaly of the point for interpolation, and the 1985 Yellow Sea height can be obtained through subtracting the height anomaly by the GPS ground height of the point. The method provided by the invention has the advantages that the continuity and smoothness problems of a current geoid grid interpolation are thoroughly solved, and the interpolation result is sole and is very high in computation accuracy. Therefore, the method can be widely used for modern height measurement.
Description
Technical field
The present invention is a kind of method for the calculating of geoid surface grid model spline interpolation, belongs to " physical geodesy " technical field in " Geodesy and Survey Engineering " subject.
Background technology
The normal level that the GPS geodetic height that certain any height anomaly is numerically equal to this point deducts this point is high.In Surveying Engineering was used, popularizing of GPS became a kind of urgent need of production so that the GPS geodetic height is converted into normal height, and height anomaly is the indispensable parameter of this conversion process.By the method that gravity and geometry combine, to refine according to tight theory first and survey the geoid's model of distinguishing, the height anomaly that calculates again unknown point is present prefered method.The present invention mainly solves the problem of calculating the unknown point height anomaly on the basis of geoid's model.Up to now, this problem has proposed three technical schemes, yet all there is the deficiency of distinct program in these three technical schemes.As everyone knows, geoid surface is continuous, smooth, a complicated curved surface.First technical scheme be in single geoid surface graticule mesh with the anti-distance weighted unknown point height anomaly interpolation of carrying out, there is serious problem in this method, namely gross distortion can occur in interpolation curved surface, curved surface disconnects, and is discontinuous, rough; Second technical scheme is a kind of easy interpolation method, during its interpolation calculation remains and carries out in single graticule mesh, but be not to adopt inverse distance weighted interpolation, but adopt linear interpolation, this method also has problems, be that interpolation result is not smooth curved surface, but pinch plane, the obvious cut-off rule of graticule mesh marginal existence is similar to folding line, and form cusp at the node place, cause curved surface rough; The 3rd technical scheme put forward by applicant, the interpolation calculation of the method is carried out in four grids, adopt the Biquadratic Polynomial match, obtain the height anomaly of unknown point through continuous cubic interpolation, but in use, we find that there be " imperial lattice phenomenon " in the Biquadratic Polynomial match, and namely there is unnecessary swing in curve, and interpolation result may be not unique, reduces Security and feasibility in causing using.Basically all be to adopt these three kinds of technical schemes at present both at home and abroad.
Patent of the present invention is the 4th technical scheme that we propose, its interpolation is carried out in nine grids, interpolation curve is five smoothing splint curves, its advantage has been to solve up hill and dale continuity and the slickness problem of geoid surface graticule mesh interpolation, interpolation result is unique, and computational accuracy is very high.
Summary of the invention
A kind of geoid surface grid model Spline Interpolation Method is characterized in that, may further comprise the steps.
L) regularization of geoid surface grid model form:
(A) regularization of indication of the present invention, comprise grid model from east to west, by the equidistant arrangement in north orientation south, graticule mesh is neat continuously;
(B) determine the lower-left of graticule mesh, upper right terrestrial coordinate;
(C) determine graticule mesh thing spacing and north and south spacing.
2) by interpolation point terrestrial coordinate, determine to participate in the graticule mesh of calculating:
(A) according to the coordinate of interpolation point, determine which graticule mesh the interpolation point drops into, write down its numbering i;
(B) determine eight graticule mesh adjacent with graticule mesh i;
(C) write down the numbering of the node of (A), (B) nine graticule mesh.
3) determine coordinate, the height anomalies of 16 of nine graticule mesh numbering nodes.
4) by its height anomaly of interpolation point Geodetic Coordinate Calculation, concrete steps are as follows:
(A) coordinate of mistake interpolation point, parallel warp or parallel are drawn parallel lines;
(B) determine four node a, b, c, the d that parallel lines and graticule mesh intersect;
(C) by the grid line at a, b, c, four node places of d, form spline curve fitting;
(a) by equidistant 4 structure minimum curvature battens, parameters comprises the number of times of splines number of times, batten correction; Read in the coordinate of known node, and be " the batten number of times adds 1 " individual known point at the end points place to the extension number, the coordinate of extension point is according to being determined by two or a consecutive point coordinate Calculation;
(b) establishing 4 nodes wanting formation curve is
,
, then connect each node
Inferior batten
Inferior polishing
Spline function curve is:
,
For the point
The height anomaly of match polishing;
Height anomaly for node;
(c)
For
The basic spline function:
, character expression is wherein pressed following calculating:
,
(d) calculate the height anomaly that polishes match point, and match is obtained comparing at the calculation level height anomaly of site position and the original height anomaly of node, if less than original node height anomaly value, then its difference is added on the original height anomaly; Otherwise, difference is reduced from the original height anomaly of node, namely the original height anomaly of node is revised;
(e) again calculate final polishing match point height anomaly with revised original node height anomaly, obtain the polishing matched curve that once more approaches original node than front;
(D) determined respectively the height anomaly of a, b, c, four nodes of d by four batten matched curves;
(E) according to the height anomaly of a, b, c, four nodes of d, by the 5th batten curve a, b, c, four nodes of d, then can determine the height anomaly of interpolation point.
2. geoid surface grid model four Spline Interpolation Method according to claim 1 also can be applicable in the quasigeoid grid model interpolation calculation.
Description of drawings
Fig. 1 geoid surface grid model nine grids five Spline Interpolation Method schematic diagram
Embodiment
Geoid's model nine grids five Spline Interpolation Method, its elementary object is based on grid model, is gone out the height anomaly value of position, arbitrfary point by the height anomaly value interpolation calculation of node.Two innovative points of the present invention are: the one, and the world proposes to adopt nine graticule mesh to carry out interpolation calculation first at home, has avoided the not unique and rough discontinuous problem of curved surface of interpolation result fully; The 2nd, in the calculating of a unknown point height anomaly, five smoothing splint curves to be introduced in the interpolation calculation of geoid surface grid model, interpolation result is reliable, and interpolation precision is very high.Principle is the smooth SPL of known points structure that equidistantly distributes according to 4, obtains the height anomaly of impact point position by five interpolation.May further comprise the steps in the implementation.
One, the regularization of geoid surface grid model form:
The grid model regularization of indication of the present invention, refer to that grid model forms the file layout of appointment: the lower-left of graticule mesh, upper right terrestrial coordinate and graticule mesh thing spacing and north and south spacing are indicated in the file first trip; The second row begins the height anomaly value for node, and from east to west, by the equidistant arrangement in north orientation south, graticule mesh is neat continuously.
Two, by interpolation point terrestrial coordinate, calculate the height anomaly of interpolation point.
1) if interpolation point terrestrial coordinate overlaps with certain node, then its height anomaly is exactly the height anomaly of node.
2) if the interpolation point falls on the line of certain two node, then its height anomaly is determined by four formed SPL of node, and these four nodes are located along the same line, and nearest with interpolation point.
3) if the interpolation point falls into the graticule mesh blank space, then determine to participate in the graticule mesh of calculating, according to the coordinate of interpolation point, determine which graticule mesh the interpolation point drops into, write down its numbering i; Determine eight graticule mesh adjacent with graticule mesh i; Write down the numbering of nine graticule mesh nodes; Determine coordinate and the height anomaly of 16 numbering nodes of nine graticule mesh.
4) at the concrete height anomaly that calculates, implementation step is as follows:
(A) coordinate of mistake interpolation point, parallel warp or parallel are drawn parallel lines, and these parallel lines stride across three nearest graticule mesh of interpolation point, and intersect at four intersection point a, b, c, d with graticule mesh;
(B) four nodes of the nearest same straight line of intersection point a form spline fit curves, thereby determine the height anomaly of intersection point a; In like manner obtain the height anomaly of intersection point b, c, other three intersection points of d.
5) the SPL constitution step is as follows:
(a) by equidistant 4 structure minimum curvature battens, parameters comprises the number of times of splines number of times, batten correction; Read in the coordinate of known node, and be " the batten number of times adds 1 " individual known point at the end points place to the extension number, the coordinate of extension point is according to being determined by two or a consecutive point coordinate Calculation;
(b) establishing the node of wanting formation curve is
,
, then connect each node
Inferior batten
Inferior polishing
Spline function curve is:
,
For the point
The height anomaly of match polishing;
Height anomaly for node;
(c)
For
The basic spline function:
, character expression is wherein pressed following calculating:
,
(d) calculate the height anomaly that polishes match point, and match is obtained comparing at the calculation level height anomaly of site position and the original height anomaly of node, if less than original node height anomaly value, then its difference is added on the original height anomaly; Otherwise, difference is reduced from the original height anomaly of node, namely the original height anomaly of node is revised;
(e) again calculate final polishing match point height anomaly with revised original node height anomaly, obtain the polishing matched curve that once more approaches original node than front.
6) interpolation point and a, b, c, four intersection points of d are on same straight line, and its height anomaly forms the match SPL by a, b, c, four intersection points of d, determine according to its interpolation of coordinate.
Claims (2)
1. a geoid surface grid model Spline Interpolation Method is characterized in that, may further comprise the steps:
L) regularization of geoid surface grid model form:
(A) regularization of indication of the present invention, comprise grid model from east to west, by the equidistant arrangement in north orientation south;
(B) determine the lower-left of graticule mesh, upper right terrestrial coordinate;
(C) determine graticule mesh thing spacing and north and south spacing;
2) by interpolation point terrestrial coordinate, determine to participate in the graticule mesh of calculating:
(A) according to the coordinate of interpolation point, determine which graticule mesh the interpolation point drops into, write down its numbering i;
(B) determine eight graticule mesh adjacent with graticule mesh i;
(C) write down the numbering of the node of (A), (B) nine graticule mesh;
4) determine coordinate, the height anomalies of 16 of nine graticule mesh numbering nodes;
5) by its height anomaly of interpolation point Geodetic Coordinate Calculation, concrete steps are as follows:
(A) coordinate of mistake interpolation point, parallel warp or parallel are drawn parallel lines;
(B) determine four node a, b, c, the d that parallel lines and graticule mesh intersect;
(C) by the grid line at a, b, c, four node places of d, form spline curve fitting;
(a) by equidistant 4 structure minimum curvature battens, parameters comprises the number of times of splines number of times, batten correction; Read in the coordinate of known node, and be " the batten number of times adds 1 " individual known point at the end points place to the extension number, the coordinate of extension point is according to being determined by two or a consecutive point coordinate Calculation;
(b) establishing 4 nodes wanting formation curve is
,
, then connect each node
Inferior batten
Inferior polishing
Spline function curve is:
,
For the point
The height anomaly of match polishing;
Height anomaly for node;
(c)
For
The basic spline function:
, character expression is wherein pressed following calculating:
,
(d) calculate the height anomaly that polishes match point, and match is obtained comparing at the calculation level height anomaly of site position and the original height anomaly of node, if less than original node height anomaly value, then its difference is added on the original height anomaly; Otherwise, difference is reduced from the original height anomaly of node, namely the original height anomaly of node is revised;
(e) again calculate final polishing match point height anomaly with revised original node height anomaly, obtain the polishing matched curve that once more approaches original node than front;
(D) determined respectively the height anomaly of a, b, c, four nodes of d by four batten matched curves;
(E) according to the height anomaly of a, b, c, four nodes of d, by the 5th batten curve, determine again the height anomaly of interpolation point.
2. geoid surface grid model four Spline Interpolation Method according to claim 1 also can be applicable in the quasigeoid grid model interpolation calculation.
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Cited By (3)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN104933291A (en) * | 2015-05-06 | 2015-09-23 | 中国石油大学(华东) | Method for the production of mean sea surface height products based on satellite altimeter data network function interpolation |
| CN110325820A (en) * | 2017-02-24 | 2019-10-11 | 赫尔环球有限公司 | Height map for indoor positioning service |
| CN111366130A (en) * | 2020-03-03 | 2020-07-03 | 山东交通学院 | Elevation anomaly interpolation and estimation method |
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2012
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Cited By (4)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN104933291A (en) * | 2015-05-06 | 2015-09-23 | 中国石油大学(华东) | Method for the production of mean sea surface height products based on satellite altimeter data network function interpolation |
| CN104933291B (en) * | 2015-05-06 | 2017-08-25 | 中国石油大学(华东) | Altimetry Data mean recovery time production method based on net―function |
| CN110325820A (en) * | 2017-02-24 | 2019-10-11 | 赫尔环球有限公司 | Height map for indoor positioning service |
| CN111366130A (en) * | 2020-03-03 | 2020-07-03 | 山东交通学院 | Elevation anomaly interpolation and estimation method |
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